Find the volumes of the solids in Exercises 65. 66. z = 4 – 4 (x² + y²) z = 1- r z = (x2 + y²)² – 1 z = -V1 67. 68. z = Vx² + y² r = 3 cos 0 r = -3 cos 0

Q: 6 write a linear homogeneous DE with constant Coefficients such that it is satisfied by the…

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Q: Let G = {(x, y): 1 ≤ x^2 + y^2 ≤ 16,0 ≤ y ≤ x). Sketch G, and find the coordinates of its centroid.

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Q: #33

A: Consider the given figure.

Q: Let S be the solid tetrahedron bounded by the four planes a = 0, y = , z = 30, and z = 4x + y. !!…

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Q: Exercise 7. Let f(2)=4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of fF…

A: Given problem is :

Q: FIs () Use spherical coordinates to evaluate 1- av where the solid E lies above the cone z=V+y*,…

A: We have to evaluate.I=∭Exzdv, using spherical coordinate  Consider, where the solid E lies above…

Q: Evaluate 1 x² + y² + z² E between the spheres x² + y² + x² + y² + z² ///₂ = dV, where E lies ² = 4…

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Q: The volume of the solid bounded by the plane 3x+6y-2z=12 and the coordinate planes is O A. 2-2y+4 1…

A: We need to find the volume of the solid bounded by the plane 3x+6y-2z=12. Now,…

Q: 3) Consider (a) Calculate the line integrals F(x, y, z) = −7+ (²²₂2) 5+ yzk 2 [ F(7) - dr Ja along…

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Q: Select the graph of the function y = [2(x– 1)]²+1. Compare the graph of this function with the graph…

A: We need to compare the two graphs.

Q: (B) By using the cylindrical coordinates, evaluate fff z √√x² + y² dV where G is the solid enclosed…

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Q: (2) Find the integral (0,2,0) and (0,0,1). where D is the tetrahedron with vertices (0,0,0),…

A: Given : ∬∫x+2y+z dV             where D is  tetrahedron with vertices 0 ,0 ,0  , 1 , 0 , 0  , 0, 2 ,…

Q: Converting into cylindrical coordinates the integral 9-2? p9-(z²+y*) ydzdrde 9-x2 9-a2

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Q: Find the Integration of 1 dx. (6x+7)6

A: To find: The integral of ∫dx6x+76. Formula used: Integration formula: Power rule of integration:…

Q: 2. Solve V'u = 0 for r<1, 0<z< T, u(r, 0, 0) = 0, a7(r, 0, 7) = 0, - u(1, 0, z) = z cos³ 0.

A: It is given that

Q: 3 dx a) 3- x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let Integrate JIS (² D (y² + x² 64 (²). dV= D = {(x, y, z) = R³ | x² + y² ≤ z²,0 ≤ z≤4}. In a…

A: We can find the triple integral.

Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: 4) Evaluate , z dV using rectangular coordinates, where Q is the solid in the first octant bounded…

A: In the first octant,  x≥0y≥0z≥0    Thus x, y and z cannot be less than 0

Q: A) Show that the function u(x; y) = 5x4y - 10 x²y³ + y5 is harmonic and determine the harmonic…

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Q: In each of the following cases, draw each solid Q bounded by the surfaces whose equations are given…

A: To graph the below surface that is in the first octant. x2=−z−3z=2y+z=3

Q: The complex potential of a line vortex of strength k centred on the origin is W=iklnz. Determine the…

A: The objective of this question is to find the complex potential of two line vortices of the same…

Q: z + 29; The value of integral (cosx,5z",6z+z sin x)·(x,y,z) ds where s is the surface of sphere x² +…

A: Please find attachment for the details solution

Q: Evaluate fff(x +y +:' dV, where a is the solid hemisphere (half of the sphere) enclosed by x +y+ =1…

A: Here in the given question, find the integration of the given function:∭Dx2+y2+z232dVWhere Ω is the…

Q: Determine the x- and y-coordinates of the centroid of the shaded area. y | -8" Answers: (X,Y)= (i 3"…

A: Figure           A(in2)         x¯(in)                          y¯(in)…

Q: The function x(u, v) (R cos(u) cos(v), R sin(u) cos(v), R sin(v)) is a local parametrization of the…

A: A Sphere of radius "R&gt;0" centered at the origin (0,0,0) is given by; S:={(x,y,z)∈ℝ3:…